Einstein’s equations look like Newton’s in the limit. It would be a little weird if we ended up having to add millions of additional parameters over the next thousand years. At the current rate we seem to get multiple years per parameter, rather than hundreds of parameters per year, right?

This kind of view tends to logically conclude in the idea of a noumenal, unknowable reality. I think it's more reasonable to say that truth itself is gold star we award to descriptions that suit our purposes. After all, descriptions are necessarily approximations (or reductive or "compressions"), since the only model of a thing with 100% fidelity is... the thing itself.

Agreed!